# Why are there 2 pi radians in a circle?

##### 1 Answer

It is not arbitrary, but it is because of the definition of radian measure.

#### Explanation:

One definition says the radian measure of angle

The arc length of the whole circle is its circumference

This definition is the reason that we have the formula for arc length

Note that whatever unit are used to measure

Also note that some teachers introduce radian measure without discussing the 'official' definition as a ratio of lengths. They simply announce that once around the circle is

This makes it look arbitrary when it is not arbitrary at all.